The present invention relates to a covering member for mounting on a fastener ring, the ring and the covering member co-operating with each other to form a fastener device for fastening a dispenser system, such as a pump or a valve, on the neck of a receptacle. The present invention also relates to a method of manufacturing such a covering member. The present invention also relates to a fluid dispenser comprising a receptacle, a dispenser system (pump or valve), and a fastener device that integrates a covering member of the invention. Such fluid dispensers are frequently used in the fields of perfumery, cosmetics, or even pharmacy.